In another copending application, Ser. No. 686,657 filed May 2, 1976, now abandoned, I have disclosed an integrated digital inter-aircraft communication and location system. Insofar as relevant to the present invention, that system individually allots to each aircraft in a given area a recurrent time slot for the emission of their navigational messages, with different carrier frequencies assigned to aircraft transmitting in consecutive time slots. The several carrier frequencies define a recurrent frame composed of a predetermined number of time slots which need not coincide with the number of intercommunicating aircraft; these time slots are established by pulses periodically emitted from an associated ground control station.
Aboard a given aircraft, the apparent velocity of another aircraft--i.e. the speed with which the two craft approach or recede from each other--can be determined on the basis of the Doppler shift, i.e. the deviation of the received carrier frequency from the nominal value of that frequency. If that Doppler shift is positive, the approach speed V.sub.d can be readily calculated. If the two craft are found to approach each other and are on the same altitude level, a possible collision course may be presumed. From the available speed and heading information, the true relative velocity can be vectorially ascertained. If the two craft are actually on a collision course, this relative velocity V.sub.r corresponds to the approach speed V.sub.d ; otherwise, V.sub.d =V.sub.r cos.alpha. where .alpha. is the angle included between the two vectors as further discussed hereinafter (at large inter-aircraft distances, however, this angle approaches zero). From the delay .DELTA.t between the arrival of a timing pulse from the ground control station and the reception of a message from the communicating aircraft to which the time slot initiated by this pulse is assigned, the first aircraft can obtain information on the minimum distance separating the two craft, that minimum distance being equal to c.DELTA.t/2 where c is the propagation velocity of the emitted radio waves. The actual distance may be considerably greater, depending upon the relative positions of the two aircraft and the ground station.
With these data, conventional arithmetic equipment aboard each aircraft can calculate a minimum closing time remaining up to the instant of closest approach; the mathematical basis for this calculation will be presented below. Such calculation, however, is valid only in first approximation, not only because of the limited reliability of the Doppler-shift evaluation (due to possible fluctuations in carrier frequency) but also in view of the aforementioned uncertainty in the determination of distance. Thus, an undue number of false alarms would result if a dropping of this minimum closing time below a certain safety threshold were taken as a signal to the crew of an aircraft to take collision-avoidance measures.